Towards Optimal Adversarial Robust Q-learning with Bellman Infinity-error

Fuente: arXiv
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Autori principali: Li, Haoran, Zhang, Zicheng, Luo, Wang, Han, Congying, Hu, Yudong, Guo, Tiande, Liao, Shichen
Natura: Preprint
Pubblicazione: 2024
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author Li, Haoran
Zhang, Zicheng
Luo, Wang
Han, Congying
Hu, Yudong
Guo, Tiande
Liao, Shichen
author_facet Li, Haoran
Zhang, Zicheng
Luo, Wang
Han, Congying
Hu, Yudong
Guo, Tiande
Liao, Shichen
contents Establishing robust policies is essential to counter attacks or disturbances affecting deep reinforcement learning (DRL) agents. Recent studies explore state-adversarial robustness and suggest the potential lack of an optimal robust policy (ORP), posing challenges in setting strict robustness constraints. This work further investigates ORP: At first, we introduce a consistency assumption of policy (CAP) stating that optimal actions in the Markov decision process remain consistent with minor perturbations, supported by empirical and theoretical evidence. Building upon CAP, we crucially prove the existence of a deterministic and stationary ORP that aligns with the Bellman optimal policy. Furthermore, we illustrate the necessity of $L^{\infty}$-norm when minimizing Bellman error to attain ORP. This finding clarifies the vulnerability of prior DRL algorithms that target the Bellman optimal policy with $L^{1}$-norm and motivates us to train a Consistent Adversarial Robust Deep Q-Network (CAR-DQN) by minimizing a surrogate of Bellman Infinity-error. The top-tier performance of CAR-DQN across various benchmarks validates its practical effectiveness and reinforces the soundness of our theoretical analysis.
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id arxiv_https___arxiv_org_abs_2402_02165
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Towards Optimal Adversarial Robust Q-learning with Bellman Infinity-error
Li, Haoran
Zhang, Zicheng
Luo, Wang
Han, Congying
Hu, Yudong
Guo, Tiande
Liao, Shichen
Machine Learning
Establishing robust policies is essential to counter attacks or disturbances affecting deep reinforcement learning (DRL) agents. Recent studies explore state-adversarial robustness and suggest the potential lack of an optimal robust policy (ORP), posing challenges in setting strict robustness constraints. This work further investigates ORP: At first, we introduce a consistency assumption of policy (CAP) stating that optimal actions in the Markov decision process remain consistent with minor perturbations, supported by empirical and theoretical evidence. Building upon CAP, we crucially prove the existence of a deterministic and stationary ORP that aligns with the Bellman optimal policy. Furthermore, we illustrate the necessity of $L^{\infty}$-norm when minimizing Bellman error to attain ORP. This finding clarifies the vulnerability of prior DRL algorithms that target the Bellman optimal policy with $L^{1}$-norm and motivates us to train a Consistent Adversarial Robust Deep Q-Network (CAR-DQN) by minimizing a surrogate of Bellman Infinity-error. The top-tier performance of CAR-DQN across various benchmarks validates its practical effectiveness and reinforces the soundness of our theoretical analysis.
title Towards Optimal Adversarial Robust Q-learning with Bellman Infinity-error
topic Machine Learning
url https://arxiv.org/abs/2402.02165